MATH 8371 Differentiable Manifolds

The course will introduce the study of smooth manifolds, fiber bundles, connections on bundles, differential forms, Lie groups, and Riemannian manifolds. This will be followed by the integration of manifolds and Stokes’ theorem, as well as de Rham cohomology. Finally, characteristic classes and aspects of Chern-Weil's theory will be introduced. Applications will include topics in gauge theory.